Does boycotting a sister, despite her attempts to reconcile through means other than verbal communication, constitute severing family ties (Qati’at al-Rahim)? And does this result in the non-acceptance of one's deeds?

Maintaining kinship ties is achieved by being good to relatives through every possible means, whether it be with money, service, visits, or greetings. As long as you continue to maintain ties with her by the means available to you, you are not severing kinship ties, and you will be rewarded by Allah Almighty. "There will always remain with you from Allah a supporter against them as long as you are upon that."